Question

A plano-convex lens is made of a material of refractive index $n$. When a small object is placed $30$ cm away in front of the curved surface of the lens, an image of double the size of the object is produced. Due to reflection from the convex surface of the lens, another faint image is observed at a distance of $10$ cm away from the lens. Which of the following statement (s) is (are) true?

• A. The refractive index of the lens is $2.5$
• B. The radius of curvature of the convex surface is $45$ cm
• C. The faint image is erect and real
• D. The focal length of the lens is $20$ cm

Answer 1

Answer: (A), (D)

The correct options are
A The refractive index of the lens is $2.5$
D The focal length of the lens is $20$ cm

Case I,

$\frac{1}{60}+\frac{1}{30}=\frac{1}{f_1}$

$f_1=20cm$

Case II,

$\frac{1}{10}-\frac{1}{30}=\frac{1}{f_2}$

$f_2=15=\frac{R}{2}$

$R=30cm$

From case I,

$f_1=\frac{R}{n-1}=20$

Thus, $n=2.5$

Radius of curvature is $30cm$

Focal length of lens is $f_1=20cm$

Answer is option A and D.